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(x³ – 1) can be factorised as: where ω is one of the cube roots of unity.

(a) (x-1) (x – ω) (x + ω2) (b) (x-1) (x – ω) (x – ω2) (c) (x-1) (x +... View Article

Solution: 8x3 + 36x2y + 54xy2 + 27y3 = (2x)3 + 3(2x)2(3y) + 3(2x)(3y)2 + (3y)3 Use identity (a+b)3 =... View Article

Solution: The antilog of a number is the inverse technique of finding the logarithm of the same number. If x... View Article

Solution: Total number of cards = 52 Given that 3 face cards of spades are removed. Remaining number of cards... View Article

Solution: We know 89 = 100 -11 Use (a-b)2 = a2 – 2ab + b2 892 = (100 – 11)2... View Article

Solution: Cost price of 12 candles = selling price of 15 candles. Let C.P of 12 candles be x. Then... View Article

(a) 2√2 (b) 4 (c) 8 (d) None of this Solution: Given 1, x, y, z, 2 are in GP.... View Article

Solution: Distance travelled by bus = 15 km 268 m = 15268 m Distance travelled by car = 7 km... View Article

Solution: We know HCF × LCM = product of given numbers 4×24 = 8a a = 4×24/8 a = 12... View Article

(a) 14 (b) 15 (c) 21 (d) 23 Solution: In this alternating repetition series, the random number 21 is repeated.... View Article

Solution: Given 2x + 3y + 4 = 0 2x + 3y = -4 …(i) x – 5y = 11... View Article

Solution: LHS = cos A/(1 + sin A) = [2 cos2(A/2) – 1]/(1 + 2 sin (A/2) cos (A/2)) =... View Article

Solution: Given numbers are 23 and 31. These are prime numbers. The LCM of two or more prime numbers is... View Article

Solution:We know sin θ = opposite side/hypotenuse Given sin θ = 7/25 cos θ = √(1 – sin2 θ) =... View Article

Solution: The first 8 multiples of 3 are 3, 6, 9, …. 8 terms This is an AP with a... View Article

AIR Spotlight is an insightful program featured daily on the All India Radio Newsonair. In this program, many eminent panellists... View Article

Nov 8th, 2021, CNA:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related POLITY AND... View Article

TABLE OF CONTENTS 1. PM to lay foundation stone of dedicated walkways for ‘Palkhi’ 2. Vice President calls for promotion... View Article

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 07th Nov 2021. Important news and... View Article

Nov 7th, 2021, CNA:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related POLITY AND... View Article